What is the maximum number of variables in a properly designed experiment?
There are an infinite number of variables in every real experiment!
I'll get a little philosophical because this is sort of a philosophical question.
An experiment's goal is to quantify the impact of one or more independent variables on a response. For example, we could measure the force we apply to a piece of wood and use the wood's deflection as the response. Ideally, this experiment would only involve one variable.
But in reality, there are a lot of variables that we are not controlling in this experiment, such as the age of the wood, where it came from, the temperature and humidity in the surrounding air at the time of the measurement, whether the wood was cut with or against the grain, and many other variables that you THINK are unimportant, like the time of day, the temperature 100 miles away, the date of your birth, etc.
Every empirical experiment contains error because uncontrolled variables can affect the experiment's outcome. Even experiments that are properly designed have error because one can use the experiment's error to determine whether the variable(s) under investigation have a statistically significant impact. Well-designed experiments attempt to control all of the independent variables that the experimenter THINKS matter. Of course, the experimenter cannot possibly and completely control all variables that DO matter.
The number of controlled variables in an experiment is another matter entirely. As far as statistics are concerned, there is no upper bound as long as one is prepared to conduct a sufficient number of experiments. Personally, I prefer to conduct at least twice as many experiments as the number of parameters I am attempting to estimate, as this enables me to estimate my error and distinguish signal from noise.
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There is no fixed maximum number of variables in a properly designed experiment, as it depends on the specific research question, experimental design, and statistical methods used. However, it is generally recommended to keep the number of variables to a minimum to reduce complexity and ensure the validity and reliability of the results.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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- Can a hypothesis that has been rejected be of any value to scientists? Why or why not?

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